In mathematics, students learn the definition of an equation: a statement that shows the values of two mathematical expressions are equal (for example, x – 5 = 10).

But math teachers, including Garrett Stern, who teaches in the Middle School, want students to understand that an equation isn’t just numbers and letters on a page. “An equation,” said Garrett, “relates to an image on the graph.”

For many of our math students, this piece of algebra art represents their pinnacle achievement in middle school math.—Garrett Stern, math teacher

These images can take a variety of forms—such as lines, parabolas, and circles—which, when placed together on a graph, can do something exciting: they can create art.

To help illustrate the visual beauty in mathematical equations, Garrett has for the past six years assigned his students the task of creating their own algebra art using the Desmos graphing calculator, a free resource used by educators around the world. Every year, he’s found that Rowland Hall students are able to produce inventive, and often very impressive, works of art.

“For many of our math students, this piece of algebra art represents their pinnacle achievement in middle school math,” said Garrett.

At an April 15 student assembly, Garrett highlighted algebra art as well as recognized the accomplishments of this year’s crop of artists. He was joined by three students, Rebecca M., Jojo P., and Erika P., who created some of the most outstanding pieces in this year’s unit. Below, these students share their algebra art experiences with the Rowland Hall community.

“Star Destroyer” by Rebecca M.

Rebecca’s drawing of a Star Destroyer is one of this year’s most complicated pieces. In fact, the Star Wars fan’s subject was so detailed that Garrett said he initially attempted to talk her out of it.

“I tried to dissuade Rebecca from trying her idea,” he remembered, “but she rejected my advice.”

Rebecca—who was inspired to tackle the Star Destroyer after viewing an algebra art drawing of an AT-AT, or All-Terrain Armored Transport, that now-junior Dillon Fang created when he took Garrett’s class—admitted that, although she was able to complete her chosen subject in the end, the process of creating the Star Destroyer was very challenging.

“I was quite confident going into this project, but my confidence began to dwindle after doing some equations,” she said. Rebecca especially remembers the difficulty of creating the ship’s bridge. “It has many small pieces that you don’t think about until you have to trace it with algebra equations.”

Rebecca said the time-consuming three to four weeks it took to complete her project required a lot of patience and resilience—but that it was worth it because it taught her she can do difficult things.

“I am super proud of it. I would gladly do it again,” said Rebecca. “I managed to push through and made a really cool design.”

“Simplicity” by Jojo P.

Jojo loves line drawings, especially of people, and discovered that she could successfully recreate the curves of a traditional ink-and-paper line drawing in the online Desmos format—an accomplishment that caught her math teacher’s attention.

“What impresses me most about Jojo's piece is the stylish curvature,” Garrett said.

But creating her project wasn’t easy. Jojo remembers feeling far behind her classmates in the early days of the assignment.

“I didn't really know how to make the equations,” she said. “In the beginning, all I had was about five lines, when everybody else had way more done. I was scared I would be behind.” Instead of panicking, however, she persisted, figuring out the equations she needed and building on her skills as she moved from long lines and wide curves to nail and flower details, which she said were definitely the hardest part of the drawing.

“When it was finished, I felt proud,” Jojo remembered. “I felt awestruck because I didn't think I could do anything like this.” It’s clear that the experience built her confidence in a way that will continue to benefit her.

“The project was challenging, but it showed me, as a mathematician, what I actually was capable of,” Jojo said.

"Ornate Owl" by Erika P.

Garrett chose to highlight Erika's piece at the assembly because she managed to include texture—although she said that hadn’t been her original plan.

“I wanted to create an owl because owls are my favorite animal, but I hadn’t planned on making it so detailed,” Erika explained.

After experimenting with equations for the owl’s body, beak, talons, and eyes, Erika said she felt like she needed to add more to her drawing and started on what turned out to be its most complicated component: feathers.

“I had to try out multiple numbers in order to get the feathers—which were created out of parabolas—to be thin and long enough to look good if I consistently spread them throughout the wings,” she said. The feathers alone took Erika over two hours to complete, and are just one example of the experimentation she had to do to create a piece that she was proud to turn in.

“The hardest part was getting shapes and lines to line up and intersect, as well as experimenting with equations to get shapes that looked at least somewhat realistic,” she remembered. “I just had to jump into it.”

Now, Erika said, she can’t imagine her drawing without those detailed additions, and she’s proud she challenged herself.

“I was glad I decided to add detail because I was thinking about submitting the work before then, but it just didn’t feel like a finished piece,” she said. “After finishing, I felt quite accomplished!"

Altogether, this year’s eighth-grade class created 75 pieces of algebra art. Below are some examples of their work (click each square to see the artwork larger on Desmos).

“Our students deservedly feel proud of their achievements,” said Garrett. “They ambitiously attempted challenging images, embraced sophisticated equations, attended to detail, and, above all, persevered.”

STEM